Oberseminar Wissenschaftliches Rechnen und Modellbildung

Profs. Bornemann/Brokate/Bungartz/Huckle/Junge

Im Wintersemester 2013/2014 fanden folgende Vorträge statt

12.02.14

14:00

Dr. Jan-Frederik Mennemann, TU Wien

02.08.011

Optimal Control of Bose Einstein Condensates

12.2.14: Optimal Control of Bose Einstein Condensates

We consider optimal control of Bose-Einstein condensates in magnetic
microtraps.
A Bose-Einstein condensate is a state of matter formed by bosons which
are cooled to temperatures very near to absolute zero.
The mean-field dynamics of a coherent Bose-Einstein condensate can be
described by the nonlinear time-dependent Gross-Pitaevskii equation.
The confining potential is parameterized by a single valued control
parameter lambda. Our aim is to find an optimal time evolution of lambda which steers the condensate from an intitial state at time zero to a desired state at
final time T. We define the objective of the control and review the optimality system.
To solve the state and adjoint equations we employ a time-splitting
spectral method or the classical Runge-Kutta method in combination with higher-order finite difference discretizations. Finally, we discuss different solvers for the minimum search to compute an optimal control. Up until now, this kind of quantum control problem has been considered in one spatial dimension only.
In this talk we explain the problems which arise if the full three-dimensional model
is considered and our strategy to solve these problems.

Abstract:
Development of real-time tools for uncertainty propagation is of increasing interest in industrial applications such as monitoring of infrastructure grids. However, it faces major challenges due to the complexity of the underlying models.
To meet these challenges we introduce a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method at the example of initial value uncertainties under deterministic dynamics and prove a consistency result.
As an application we discuss arsenate transportation and adsorption in drinking water grids. For this purpose the novel method is extended to a model system of partial differential and algebraic equations, and our results are compared to Monte Carlo computations.

28.01.13: Metastable Decompositions - About conformation dynamics and an application to modular networks

Abstract:
Approximately 16 years ago, the idea emerged to construct Markov chain models for reversible, time-continuous Markov processes using metastable decompositions of the state space.
In the first part of the talk, we will show a functional analytic point of view, which interprets the approach as a discretization of the associated transfer operator by Galerkin projection. This will allow for an error analysis and adaptive refinement concepts for the discretization. Surprisingly, it will turn out that it is also possible to avoid such a refinement while even enhancing the approximation quality at the same time.
In the second part of the talk, we will discuss how one can use this framework for the analysis of modular networks. Particularly, we will outline an algothmic strategy for efficient module identification in networks and talk about the possibilities of hierarchical soft clustering.